Asymptotic regression model

#1
Hi all, fairly new to statistics, so apologies in advance if the below is not suitable for this forum.

I have a data set in which the behavior is fairly asymptotic with 0 over time.

I'm wondering what would be the best type of regression model to fit this data given that logarithmic regressions are undefined at 0.

My initial thoughts are using a power model or to alter the 0-time points to be slightly positive, but any more experienced input would be more than welcome.

Thanks!

Example of data:
RAVE_BVAS_v_Time.png
 

Dason

Ambassador to the humans
#2
Most likely you're worried about the logs being 0 because you're thinking of transforming your raw data. If you use a model that has an exponential/logarithmic trend for the mean but doesn't require the data itself to be transformed that would be ideal. If that sounds good to you then you'll probably want to look into GLMs (generalized linear models). It kind of looks like your response is a count in which case a Poisson or Negative Binomial distribution for the response might make sense.
 
#3
Hi Dason,

Thanks for your reply, I think the use of GLM is probably right as this data is strictly non-negative, however, I don't think a Poisson distribution is quite right as the BVAS score is a discontinuous (e.g., whole numbers only) metric that ranges of 0-36. The points shown are not counts but rather represent individual patients.

Knowing this - what model do you think would best be used to generate a fit?

Many thanks!